HV-LSC-ex$$^2$$: velocity field interpolation using extended least-squares collocation

Abstract Least-squares collocation (LSC) is a widely used method applied in physical geodesy to separate observations into signal and noise part but has received only little attention when interpolating velocity fields. The advantage of the LSC possibility filter interpolate as well extrapolate observations. Here, we will present several extensions traditional technique, which allows combined interpolation both horizontal components (horizontal (HV)-LSC), separation on different tectonic plates, removal stationarity by moving variance (the latter HV-LSC-ex(tended) $$^2$$ 2 ). Furthermore, covariance analysis, required find necessary input parameters for LSC, extended finding suitable correlation length using at same time. all are tested synthetic dataset known newly defined points, with stations separated four plates distinct plate velocities. methodologies evaluated calculation misfit data, implementation leave-one-out cross-validation Jackknife resampling. largest improvement terms reduced stability can be obtained boundaries considered. In addition, any small-scale changes filtered out moving-variance approach smoother field obtained. comparison Kriging method, fit better new HV-LSC-ex technique.